Adaptive Control of Combustion Instabilities for Non-Minimum Phase Systems

Abstract

Model-based adaptive controllers, or self-tuning regulators, offer an efficient means of stabilising combustion instabilities over a range of operating conditions. They utilise some general properties satisfied by a wide range of combustion systems and thus avoid the need for on-line system identification. One of the required properties is that the open-loop system is minimum-phase i.e. that it does not contain any right-half plane (RHP) zeros. It is shown in this work that for some combustion systems in which a pressure measurement is used as a sensor signal, right-half plane zeros arise due to reflections from boundaries. This may either occur due to the reflection of acoustic waves, or due to the acceleration of entropy waves. A method of eliminating the right-half plane zeros by using a modified pressure measurement is proposed, which also maintains the relative degree of the system. The modified sensor signal is applied to numerical models of unstable combustion systems with large reflections from boundaries, and the self-tuning regulator is demonstrated to work in cases where it fails with a single pressure measurement. This is demonstrated for several different unstable combustion systems, confirming that the approach remains independent of the system details.